We report on the fabrication and optical properties of thin metal films periodically patterned with square hole arrays of 2 micron pitch, which behave as substrateless plasmonic devices at mid-infrared frequencies. Large (3×3 mm2) meshes were fabricated by metallizing a patterned silicon nitride membrane. The mid-infrared spectra display resonant absorption lines with a Q-factor up to 22 in both transmission and reflection, due to the interaction of the radiation with surface plasmon modes on both faces of the film, allowed by substrate removal. The devices can be used to fabricate surface plasmon-based chemical sensors employing mid-infrared radiation.